Efficient estimation of linear functionals in emission tomography
- Lawrence Berkeley National Lab., CA (United States)
In emission tomography, the spatial distribution of a radioactive tracer is estimated from a finite sample of externally detected photons. The author presents an algorithm-independent theory of statistical accuracy attainable in emission tomography that makes minimal assumptions about the underlying image. Let f denote the tracer density as a function of position (i.e., f is the image being estimated). He considers the problem of estimating the linear functional {Phi}(f) {equivalent_to} {integral}{phi}(x)f(x)dx, where {phi} is a smooth function, from n independent observations identically distributed according to the Radon transform of f. Assuming only that f is bounded above and below away from 0, he constructs statistically efficient estimators for {Phi}(f). By definition, the variance of the efficient estimator is a best-possible lower bound (depending on {phi} and f) on the variance of unbiased estimators of {Phi}(f). The results show that, in general, the efficient estimator will have a smaller variance than the standard estimator based on the filtered-backprojection reconstruction algorithm. The improvement in performance is obtained by exploiting the range properties of the Radon transform.
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Insts. of Health, Bethesda, MD (United States)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 477280
- Journal Information:
- SIAM Journal of Applied Mathematics, Vol. 57, Issue 2; Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
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